The interacton equation

Given the Lie algebra fp of vector fields of a free particle then in a joint field of interacting particles an interacton is defined as a direct summand isomorphic to fp. For several soliton equations it is shown how interactons can be obtained from various methods of symmetry analysis and how their dynamics can be expressed in terms of self-interaction alone; this procedure leads to new integrable systems. Furthermore, in case of nonlinear Schrödinger equations it is shown how the dynamics of interactons can be formulated in terms of self-consistent potentials with antlinear parts.